Carbon taxes are the way to go.
Why? Because they allow governments to set policy empirically. You can raise the tax a little, bit-by-bit, until you start seeing negative effects. Carbon taxes allow a legislature of non-economists to procedurally find the maximum reduction that the economy can bear, which is good, because obviously you don't want more than that, and given the nature of the situation you probably don't want less.
The difference between this and a cap-and-trade model is that with cap-and-trade, there's a lot of money tied up in the carbon shares allocated, so lowering the cap is politically impossible. Big corporations like it because they have an easier time acquiring carbon credits than small companies, because they have political influence.
https://en.wikipedia.org/wiki/Carbon_emission_trading#Incent...
Cap-and-trade worked with other kinds of emissions because those emissions are less common and come only from certain industries, whereas carbon comes from everywhere. As such, it wasn't possible for the acid rain producers to lobby Congress to raise the cap on NOx. Or to not lower it. Furthermore, the market is small enough that it was possible for charitable organizations to make a dent by buying emissions allowances and "retiring" them -- which is extremely unlikely to matter for carbon given the size of the carbon market.
Carbon taxes are fairer and simpler, and it's harder for a company to weasel out. Some observers have suggested that an industry could lobby to be exempt, but this seems unlikely: how many industries have successfully exempted themselves from income tax? From VAT? By contrast, this happened:
https://www.scientificamerican.com/article/carbon-credits-sy...
> a diplomatic cable published last month by the WikiLeaks website reveals that most of the CDM projects in India should not have been certified because they did not reduce emissions beyond those that would have been achieved without foreign investment. Indian officials have apparently known about the problem for at least two years.
>[...] Today, more than 720 Indian projects have been approved and have gained some 120 million tonnes' worth of carbon credits, a large fraction of the 750 million tonnes issued since 2005 (see 'Cleaning up').
> Yet on the evidence of discussions at the meeting, most of the carbon-offset projects in India fail to meet the CDM requirements set by the UN Framework Convention on Climate Change.